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C₂×#34474 #7626076

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

8550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

(1,2);(3,4,6,5)(7,8,10,12)(9,13,14,11)(15,16)(17,20)(18,23)(19,24)(21,25)(22,27)(26,28)(29,30);(7,8,10,12)(9,11,14,13)(16,17)(18,25)(22,24)(26,30);(7,8)(9,11)(10,12)(13,14)(15,17,20,16)(18,23,25,21)(19,24,27,22)(26,29,30,28);(3,5,6,4)(7,9,10,14)(8,11,12,13)(15,18)(16,21)(17,23)(19,26)(20,25)(22,28)(24,29)(27,30);(15,19,20,27)(16,22,17,24)(18,26,25,30)(21,28,23,29)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533272);